"The kid's very quick. He's definitely very quick, very naturally talented. He certainly has a lot to learn, he's got a steep learning curve, but 100 percent he's there on talent," the Briton told Reuters at the Indian Grand Prix.
Kvyat has been racing for the MW Arden GP3 team which Horner owns jointly with Red Bull's Australian race driver Mark Webber. The Russian is currently second and seven points behind Argentine Facu Regalia.
Toro Rosso, who are effectively Red Bull's junior team, announced on Monday that the 19-year-old would replace Daniel Ricciardo when the Australian graduates to the world champions next season as Webber's successor.
The news came as a surprise to the Formula One paddock, with Portugal's Antonio Felix Da Costa previously seen as the favourite.
Some commentators have suggested that the allure of the Russian market to the Austrian energy drink maker may have influenced the decision, particularly with Russia hosting a Formula One race for the first time next year, but Horner said it came down to results.
"If the decision had been made 12 months ago, Antonio would have been the clear-cut choice. But Antonio's had an indifferent year this year and Daniil has really excelled and that's what gave him the nod over Antonio," said Horner.
Some of those who will be racing Kvyat next season suggested it might be too much, too early however.
"Of course he is thinking it is a great break and he is going to race in F1 but if you could have the choice of entering F1 at 19 after a year in F3 and GP3, or doing a couple of years in a different category, you would definitely go for a couple more years," said 2009 world champion Jenson Button.
"That way you could learn a lot more about slicks and wings... and learn a lot more of the circuits you race on, and the way an F1 team goes racing," added the McLaren driver, who made his debut with Williams in 2000 as a 20-year-old.
"There is so much to learn that I didn't understand when I came into the sport and it is a real shock for someone at 19, who has to also learn to drive an F1 car and have to work with a KERS (energy recovery) power unit, which is completely new and alien to most of us."
Britain's Paul Di Resta, whose future at Force India remains uncertain, said he was baffled by Toro Rosso's move.
"I think I was as shocked as anyone," the Scot told reporters. "I was expecting one person to get the drive, but again it is not easy to predict this game at the moment, is it?
"Unfortunately that is where the midfield is. Nothing makes sense.
"It is a big year, and it is a big ask for someone who is 19," he continued. "But he might come out of the box and shock us all. I don't underestimate anyone coming in but it is a big jump from GP3 to come into F1 and a new regulation change. It was busy enough without it already getting busier next year."
Lewis Hamilton, the 2008 world champion for McLaren and now at Mercedes, was less fussed.
"Kimi (Raikkonen, the 2007 champion with Ferrari) came from Formula Renault," he said. "We haven't got any other Kimis out there but Kimi showed that it is possible.
"I won everything on the way up and even when I was in Formula Three I wasn't ready for Formula One. I was only just ready after I won GP2. But everyone's different. It's a big ask for anyone that comes into Formula One."
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